Spectral analysis with Audacity

Spectral analysis is a tool that can be very useful for the musician or the luthier, for example:

- For the fine analysis of an existing musical instrument, for the purpose of its possible reproduction or its adjustment.

- For the analysis of the resonance of a plate, such as a violin top plate or a violin back for example. This practice, known as tap tuning, is
quite controversial in the community of luthiers, because it is quite difficult to master...
But the resonance of a piece can be seen as its sound signature, and even if it is difficult to predict the behavior of the finished instrument,
it is very useful, for the luthier's archiving, to keep this trace, for purposes of repeatability and comparison, for
future constructions.

- For the musician who may have difficulty transcribing too fast or too confusing pieces.

- For the musicologist, to analyze the singing of a particular performer or an instrumentalist.

Spectral analysis was in the past a technique reserved for laboratories, and required expensive equipment
and some training in interpreting the results.

Today we are fortunate to have access to high-performance digital tools with free access.
For what we are concerned here, I want to talk about Audacity.
I already had the opportunity to introduce Audacity, see the article in the section The softwares that I use

I propose a tutorial that shows how you can use Audacity to analyze the song of a traditional Breton singer, André Drumel.
Didier Jaffredo, host of the forum FFIAC (French Forum of Irish Whisle Makers) has set the pretty nice project
to create a flute respecting the original range used by this singer.

Opening the MP3 file in Audacity. The two blue curves visualize the sound signal of the two channels of this stereo file.
We already visualize the phrasing, ie the separation of syllables.

We will work first on the first syllables.
1- Select the first syllables.
2- Zoom in on the selection.

1- You can simply listen to a selected part: select, then press the spacebar.
2- In order to find your way around and to record the results, it is useful to insert a "markers" track
Track menu ... / Add New ... / Markers Track .
Then click in the marker track and type some text.
One can for example transcribe the syllables sung and note the measured frequencies.

Analysis of a note.
1 - After careful listening, select a stable part of a note.
It is crucial to avoid the attack and the fall of the note.
Select the widest possible area, which corresponds to as many samples as possible.
2 - Menu Analysis / Plot spectrum ...

"Frequency Analysis" Window
1- Keep these settings.
The Size parameter corresponds to the number of samples taken into account. The greater the number, the finer and detailed the analysis will be.
8192 is an interesting value, but if the note is too short, you can be forced to adopt 4096, see 2048.
2 - The frequency peaks correspond to the frequencies mainly present in the selected sample.
Walk the cursor near these peaks.
3- The software detects in this zone the nearest peak and gives the frequency, as well as the closest corresponding note
(be careful, this approximation is not sufficient, see the next step).
4 - We often find, for a dominant frequency, several harmonics like here, the lower octave and
the upper octave.
5 - In the same way we find here the fifth.

On this same site, - link here -, I have developed this little tool which is complementary to Audacity
in order to get a finer analysis of the measured frequency.
We enter the frequency, and possibly a pitch value for the A4 reference.
And we get a display identical to the one we would have with a chromatic tuner,
giving the note, and its deviation in cents.
The cent represents a hundredth of a semitone.

Here is a typical example of the spectrum of a sung note.
We find three harmonics of the C#, on three different octaves (C#4, C#5 and C#6).
There is also the fifth of C#5 which is G#5.
It is deduced here that the perceived note is the C#5, which is the most
represented in this spectrum.
Attention, this is not an absolute rule, the human ear has a perception of frequencies
that can be disturbing sometimes, and the perceived note is not always the note
at the highest peak.
Of course, you have to confront this analysis with a careful listening of the note.

Here is another phenomenon that we often find on sung voice and on instruments,
this is an example of vibrato where the singer vibrates his note over the duration of the sample.
The peaks have two heads, corresponding to the alternation between the two frequencies distant from about a semi-tone.

Here is the example of the analysis of a complete sentence.
We must continue this type of analysis on a larger part of the piece for
to draw conclusions, on the scale used for example.